A013524 Numerator of [x^(2n+1)] of the Taylor expansion tanh(cosec(x) - cot(x)).

1, 0, -1, -1, -1, 13, 7951, 21599, -294997, -275833, -60527057, -6338125867, 37620769159, 10425684579701, 5113538085001361, -25594556368763237, -6013201989263028181, -3771502911169983097219, 18335649295377317231411, 669255665793644548301365603

Offset: 0

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Keywords

• sign
• frac

Comments

The e.g.f. of x/2, tanh(cosec(x) - cot(x)) = x/(2^1*1!) - 8*x^5/(2^5*5!) - 112*x^7/(2^7*7!) - 128*x^9/(2^9*9!) + 109824*x^11/(2^11*11!) + ... is (up to signs) apparently provided by A003721.

Examples

			Series starts: x/2 - x^5/480 - x^7/5760 - x^9/1451520 + 13*x^11/9676800 + 7951*x^13/49816166400 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..200

Programs

Maple

ser := series(tanh(tan(x/2)), x, 40):
seq(numer(coeff(ser, x, 2*n+1)), n=0..19); # Peter Luschny, Nov 14 2016

Mathematica

Numerator[Take[CoefficientList[Series[Tanh[Csc[x] - Cot[x]], {x,0,40}], x], {2, -1, 2}]] (* G. C. Greubel, Nov 12 2016 *)

Formula

a(n) = numerator([x^(2*n+1)] tanh(tan(x/2))). - Peter Luschny, Nov 14 2016

Extensions

Name edited by R. J. Mathar, Dec 19 2011